Question

finding the slope of a line

use the information provided to find the slope of each line. state what the slope represents.

1
seconds | 0 | 5 | 10
feet | 0 | 30 | 60
2
hours | 0 | 2 | 5
dollars | 0 | 18 | 45

Explanation:

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Calculate slope for Table 1

Use points $(0,0)$ and $(5,30)$:
$m_1 = \frac{30 - 0}{5 - 0} = \frac{30}{5} = 6$

Step3: Interpret slope for Table 1

The slope represents feet per second, so 6 feet per second.

Step4: Calculate slope for Table 2

Use points $(0,0)$ and $(2,18)$:
$m_2 = \frac{18 - 0}{2 - 0} = \frac{18}{2} = 9$

Step5: Interpret slope for Table 2

The slope represents dollars per hour, so 9 dollars per hour.

Answer:

1. Slope: $6$, which represents a speed of 6 feet per second.
2. Slope: $9$, which represents a rate of 9 dollars per hour.